Exam 8: Sets and Logic

Specify the set by description. $\{ 40,400,4,000 , \ldots \}$

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,9\} C=\{2,5,6,9,10\} List all the members of the set. $( A \cap B ) \cap C$

Construct a truth table for the statement. cellpadding ="0" cellspacing ="0" width ="62\%" border ="1"> pqp\wedgeq

How many subsets does the set $\{ 1,3,5,7 \}$ have?

Let U=\{1,2,3,4,5,6,7\} A=\{1,2,3,4\} B=\{2,3,5,7\} C=\{3,5,7\} List all the members of the set. $A \cap C$

Specify the set by description. $\{ l , u , n , c , h \}$

Let U be the universal set. If $C \subset D$ , describe the following set. $C \cup D$

Tell whether you believe that the conjecture is true or false. The basic metric units for length, volume, and weight are larger than their U.S. counterparts.

Answer the question and tell whether it illustrates inductive or deductive reasoning. Give the $50 \text { th }$ number in the pattern: $1,4,9,16,25 , \ldots$

Use set notation to identify the shaded portion of the Venn diagram.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{7,9\} C=\{2,7,8,9,10\} List all the members of the set. $( A \cup B ) \cup C$

List all subsets of the given set. Identify any of the subsets that are improper. $\{ 4,8,9 \}$

Let U=\{1,2,3,4,5,6,7\} A=\{1,2,3,4\} B=\{2,3,5,7\} C=\{1,3,7\} List all the members of the set. $\bar { A }$

The following is a statement. It rained on Tuesday.

A poll was taken of $100$ students at a commuter campus to find out how they got to campus. The results were: $42$ said they drove alone. $31$ rode the bus. $29$ rode in a carpool. $8$ used both carpools and rode the bus. $11$ used both a carpool and sometimes drove alone. $6$ used buses as well as drove alone. $3$ used all three methods. How many are not using any of the three (Region VIII)? A = {people who drive alone} B = {people who ride the bus} C = {people who carpool} Use the figure (with Regions I to VIII) to answer the question. __________ students

Use Venn diagrams to check the validity of the argument. Some cats can talk. Some cats can meow. Therefore, some animals that meow can talk. _______________ ( valid / not valid)

Draw a Venn diagram showing the sets $A$ and $B$ where $A$ is the set of people who have had their wisdom teeth removed, $B$ is the set of people who have had their appendix removed, and the universe is the set of all people. Assume that each region corresponds to a nonempty set.

List all subsets of the following set. $H = \{ 4 \}$

In a recent survey of $100$ women, the following information was gathered: $59$ use shampoo A. $51$ use shampoo B. $35$ use shampoo C. $24$ use shampoos A and B. $19$ use shampoos A and C. $14$ use shampoos B and C. $11$ use all three. How many are using shampoo B only (Region II)? A = {women who use shampoo A } B = {women who use shampoo B } C = {women who use shampoo C } Use the figure (with Regions I to VIII) to answer the question. __________ women

A survey of 800 members of a club asked the following questions: Check the box if the answer is "yes". I watched a movie at a theater in the past month. I watched a rented movie at home in the past month. If 185 respondents checked the first box, what percent of the respondents watched a movie at a theater in the past month? If 330 respondents checked the second box, what percent of the respondents watched a rented movie at home in the past month? If 65 checked both boxes, what percent of the respondents watched movies both in a theater and at home? What percent of the members watched a movie in a theater or at home in the past month? Round your answers to the nearest tenth of a percent. Select the correct answer.